Preheat the oven to 350°F and grease a 6-inch round cake pan. In a mixing bowl, cream the 1/2 cup softened butter with the granulated sugar until light. Add the eggs one at a time, then stir in 2 teaspoons vanilla.
In a separate bowl, whisk the flour, baking powder, and salt. Add half the dry mix to the butter mixture, followed by half the milk. Repeat with the remaining dry mix and milk until just combined.
Pour the batter into the pan and bake for 25-30 minutes until a toothpick comes out clean. Cool the cake in the pan for 10 minutes, then turn it out onto a wire rack to cool completely.
For the buttercream, beat the 1 cup softened butter in a clean mixing bowl until smooth. Gradually add the powdered sugar, then the remaining 2 tablespoons milk and 2 teaspoons vanilla. Beat until fluffy.
Place the cooled cake on a plate and spread a thin layer of buttercream over the top and sides. Fit a piping bag with a flat or ribbon tip and pipe thin horizontal strips across the cake to look like bandages.
Press the candy eyes onto the cake where the strips allow them to show through.